272179
For distance far away from centre of dipole the change in magnitude of electric field with change in distance from the centre of dipole is:
1 zero.
2 same in equatorial plane as well as axis of dipole.
3 more in case of equatorial plane of dipole as compared to axis of dipole.
4 more in case of axis of dipole as compared to equatorial plane of dipole.
Explanation:
(d) For distances far away from centre of dipole
$~{{E}_{axis~}}={{E}_{a}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{2p}{{{r}^{3}}},{{E}_{equa~}}={{E}_{e}}=\frac{1}{4\pi {{\varepsilon }_{0}}}-\frac{p}{{{r}^{3}}}~~\frac{d}{dr}\left( {{E}_{a}} \right)=\frac{1}{4\pi {{\varepsilon }_{0}}}2p\frac{d}{dr}\left( {{r}^{-3}} \right)=-6\cdot \frac{1}{4\pi {{\varepsilon }_{0}}}\frac{p}{{{r}^{4}}}~$
$\frac{d}{dr}\left( {{E}_{c}} \right)=\frac{1}{4\pi {{\varepsilon }_{0}}}p\frac{d}{dr}\left( {{r}^{-3}} \right)=-3\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{p}{{{r}^{4}}}$
From equations (i) and (ii) the magnitude of change in electric field w.r.t. distance is more in case of axis of dipole as compared to equatorial plane.
NCERT Page-27 / N-24
Electric Charges and Fields
272180
Electric field at a point on equatorial line of a dipole & direction of the dipole moment
1 will be parallel
2 will be in opposite direction
3 will be perpendicular
4 are not related
Explanation:
(b) The direction of electric field at equatorial point $A$ or $B$ will be in opposite direction, as that of direction of dipole moment:
NCERT Page-27/N-24
Electric Charges and Fields
272181
If a dipole of dipole moment $\vec{p}$ is placed in a uniform electric field $\vec{E}$, then torque acting on it is given by
1 $\vec{\tau }=\vec{p}.\vec{E}$
2 $\vec{\tau }=\vec{p}\times \vec{E}$
3 $\vec{\tau }=\vec{p}+\vec{E}$
4 $\vec{\tau }=\vec{p}-\vec{E}$
Explanation:
(b) Given : Dipole moment of the dipole $=\vec{p}$ and uniform electric field $=\vec{E}$. We know that dipole moment (p) $=q\cdot a$ (where $q$ is the charge and $a$ is dipole length). And when a dipole of dipole moment $\vec{p}$ is placed in uniform electric field $\vec{E}$, then Torque $\left( \tau \right)=$ Either force $\times $ perpendicular distance between the two forces $=qqasin\theta $ or $\tau =pEsin\theta $ or $\vec{\tau }=\vec{p}\times \vec{E}$ (vector form).
NCERT Page-28 / N-27
Electric Charges and Fields
272182
If ${{E}_{a}}$ be the electric field strength of a short dipole at a point on its axial line and ${{E}_{e}}$ that on the equatorial line at the same distance, then
1 ${{E}_{e}}=2{{E}_{a}}$
2 ${{E}_{a}}=2{{E}_{e}}$
3 ${{E}_{a}}={{E}_{e}}$
4 None of these
Explanation:
(b) We have ${{E}_{a}}=\frac{2kp}{{{r}^{3}}}$ and ${{E}_{e}}=\frac{kp}{{{r}^{3}}};\therefore {{E}_{a}}=2{{E}_{e}}$.
272179
For distance far away from centre of dipole the change in magnitude of electric field with change in distance from the centre of dipole is:
1 zero.
2 same in equatorial plane as well as axis of dipole.
3 more in case of equatorial plane of dipole as compared to axis of dipole.
4 more in case of axis of dipole as compared to equatorial plane of dipole.
Explanation:
(d) For distances far away from centre of dipole
$~{{E}_{axis~}}={{E}_{a}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{2p}{{{r}^{3}}},{{E}_{equa~}}={{E}_{e}}=\frac{1}{4\pi {{\varepsilon }_{0}}}-\frac{p}{{{r}^{3}}}~~\frac{d}{dr}\left( {{E}_{a}} \right)=\frac{1}{4\pi {{\varepsilon }_{0}}}2p\frac{d}{dr}\left( {{r}^{-3}} \right)=-6\cdot \frac{1}{4\pi {{\varepsilon }_{0}}}\frac{p}{{{r}^{4}}}~$
$\frac{d}{dr}\left( {{E}_{c}} \right)=\frac{1}{4\pi {{\varepsilon }_{0}}}p\frac{d}{dr}\left( {{r}^{-3}} \right)=-3\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{p}{{{r}^{4}}}$
From equations (i) and (ii) the magnitude of change in electric field w.r.t. distance is more in case of axis of dipole as compared to equatorial plane.
NCERT Page-27 / N-24
Electric Charges and Fields
272180
Electric field at a point on equatorial line of a dipole & direction of the dipole moment
1 will be parallel
2 will be in opposite direction
3 will be perpendicular
4 are not related
Explanation:
(b) The direction of electric field at equatorial point $A$ or $B$ will be in opposite direction, as that of direction of dipole moment:
NCERT Page-27/N-24
Electric Charges and Fields
272181
If a dipole of dipole moment $\vec{p}$ is placed in a uniform electric field $\vec{E}$, then torque acting on it is given by
1 $\vec{\tau }=\vec{p}.\vec{E}$
2 $\vec{\tau }=\vec{p}\times \vec{E}$
3 $\vec{\tau }=\vec{p}+\vec{E}$
4 $\vec{\tau }=\vec{p}-\vec{E}$
Explanation:
(b) Given : Dipole moment of the dipole $=\vec{p}$ and uniform electric field $=\vec{E}$. We know that dipole moment (p) $=q\cdot a$ (where $q$ is the charge and $a$ is dipole length). And when a dipole of dipole moment $\vec{p}$ is placed in uniform electric field $\vec{E}$, then Torque $\left( \tau \right)=$ Either force $\times $ perpendicular distance between the two forces $=qqasin\theta $ or $\tau =pEsin\theta $ or $\vec{\tau }=\vec{p}\times \vec{E}$ (vector form).
NCERT Page-28 / N-27
Electric Charges and Fields
272182
If ${{E}_{a}}$ be the electric field strength of a short dipole at a point on its axial line and ${{E}_{e}}$ that on the equatorial line at the same distance, then
1 ${{E}_{e}}=2{{E}_{a}}$
2 ${{E}_{a}}=2{{E}_{e}}$
3 ${{E}_{a}}={{E}_{e}}$
4 None of these
Explanation:
(b) We have ${{E}_{a}}=\frac{2kp}{{{r}^{3}}}$ and ${{E}_{e}}=\frac{kp}{{{r}^{3}}};\therefore {{E}_{a}}=2{{E}_{e}}$.
272179
For distance far away from centre of dipole the change in magnitude of electric field with change in distance from the centre of dipole is:
1 zero.
2 same in equatorial plane as well as axis of dipole.
3 more in case of equatorial plane of dipole as compared to axis of dipole.
4 more in case of axis of dipole as compared to equatorial plane of dipole.
Explanation:
(d) For distances far away from centre of dipole
$~{{E}_{axis~}}={{E}_{a}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{2p}{{{r}^{3}}},{{E}_{equa~}}={{E}_{e}}=\frac{1}{4\pi {{\varepsilon }_{0}}}-\frac{p}{{{r}^{3}}}~~\frac{d}{dr}\left( {{E}_{a}} \right)=\frac{1}{4\pi {{\varepsilon }_{0}}}2p\frac{d}{dr}\left( {{r}^{-3}} \right)=-6\cdot \frac{1}{4\pi {{\varepsilon }_{0}}}\frac{p}{{{r}^{4}}}~$
$\frac{d}{dr}\left( {{E}_{c}} \right)=\frac{1}{4\pi {{\varepsilon }_{0}}}p\frac{d}{dr}\left( {{r}^{-3}} \right)=-3\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{p}{{{r}^{4}}}$
From equations (i) and (ii) the magnitude of change in electric field w.r.t. distance is more in case of axis of dipole as compared to equatorial plane.
NCERT Page-27 / N-24
Electric Charges and Fields
272180
Electric field at a point on equatorial line of a dipole & direction of the dipole moment
1 will be parallel
2 will be in opposite direction
3 will be perpendicular
4 are not related
Explanation:
(b) The direction of electric field at equatorial point $A$ or $B$ will be in opposite direction, as that of direction of dipole moment:
NCERT Page-27/N-24
Electric Charges and Fields
272181
If a dipole of dipole moment $\vec{p}$ is placed in a uniform electric field $\vec{E}$, then torque acting on it is given by
1 $\vec{\tau }=\vec{p}.\vec{E}$
2 $\vec{\tau }=\vec{p}\times \vec{E}$
3 $\vec{\tau }=\vec{p}+\vec{E}$
4 $\vec{\tau }=\vec{p}-\vec{E}$
Explanation:
(b) Given : Dipole moment of the dipole $=\vec{p}$ and uniform electric field $=\vec{E}$. We know that dipole moment (p) $=q\cdot a$ (where $q$ is the charge and $a$ is dipole length). And when a dipole of dipole moment $\vec{p}$ is placed in uniform electric field $\vec{E}$, then Torque $\left( \tau \right)=$ Either force $\times $ perpendicular distance between the two forces $=qqasin\theta $ or $\tau =pEsin\theta $ or $\vec{\tau }=\vec{p}\times \vec{E}$ (vector form).
NCERT Page-28 / N-27
Electric Charges and Fields
272182
If ${{E}_{a}}$ be the electric field strength of a short dipole at a point on its axial line and ${{E}_{e}}$ that on the equatorial line at the same distance, then
1 ${{E}_{e}}=2{{E}_{a}}$
2 ${{E}_{a}}=2{{E}_{e}}$
3 ${{E}_{a}}={{E}_{e}}$
4 None of these
Explanation:
(b) We have ${{E}_{a}}=\frac{2kp}{{{r}^{3}}}$ and ${{E}_{e}}=\frac{kp}{{{r}^{3}}};\therefore {{E}_{a}}=2{{E}_{e}}$.
272179
For distance far away from centre of dipole the change in magnitude of electric field with change in distance from the centre of dipole is:
1 zero.
2 same in equatorial plane as well as axis of dipole.
3 more in case of equatorial plane of dipole as compared to axis of dipole.
4 more in case of axis of dipole as compared to equatorial plane of dipole.
Explanation:
(d) For distances far away from centre of dipole
$~{{E}_{axis~}}={{E}_{a}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{2p}{{{r}^{3}}},{{E}_{equa~}}={{E}_{e}}=\frac{1}{4\pi {{\varepsilon }_{0}}}-\frac{p}{{{r}^{3}}}~~\frac{d}{dr}\left( {{E}_{a}} \right)=\frac{1}{4\pi {{\varepsilon }_{0}}}2p\frac{d}{dr}\left( {{r}^{-3}} \right)=-6\cdot \frac{1}{4\pi {{\varepsilon }_{0}}}\frac{p}{{{r}^{4}}}~$
$\frac{d}{dr}\left( {{E}_{c}} \right)=\frac{1}{4\pi {{\varepsilon }_{0}}}p\frac{d}{dr}\left( {{r}^{-3}} \right)=-3\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{p}{{{r}^{4}}}$
From equations (i) and (ii) the magnitude of change in electric field w.r.t. distance is more in case of axis of dipole as compared to equatorial plane.
NCERT Page-27 / N-24
Electric Charges and Fields
272180
Electric field at a point on equatorial line of a dipole & direction of the dipole moment
1 will be parallel
2 will be in opposite direction
3 will be perpendicular
4 are not related
Explanation:
(b) The direction of electric field at equatorial point $A$ or $B$ will be in opposite direction, as that of direction of dipole moment:
NCERT Page-27/N-24
Electric Charges and Fields
272181
If a dipole of dipole moment $\vec{p}$ is placed in a uniform electric field $\vec{E}$, then torque acting on it is given by
1 $\vec{\tau }=\vec{p}.\vec{E}$
2 $\vec{\tau }=\vec{p}\times \vec{E}$
3 $\vec{\tau }=\vec{p}+\vec{E}$
4 $\vec{\tau }=\vec{p}-\vec{E}$
Explanation:
(b) Given : Dipole moment of the dipole $=\vec{p}$ and uniform electric field $=\vec{E}$. We know that dipole moment (p) $=q\cdot a$ (where $q$ is the charge and $a$ is dipole length). And when a dipole of dipole moment $\vec{p}$ is placed in uniform electric field $\vec{E}$, then Torque $\left( \tau \right)=$ Either force $\times $ perpendicular distance between the two forces $=qqasin\theta $ or $\tau =pEsin\theta $ or $\vec{\tau }=\vec{p}\times \vec{E}$ (vector form).
NCERT Page-28 / N-27
Electric Charges and Fields
272182
If ${{E}_{a}}$ be the electric field strength of a short dipole at a point on its axial line and ${{E}_{e}}$ that on the equatorial line at the same distance, then
1 ${{E}_{e}}=2{{E}_{a}}$
2 ${{E}_{a}}=2{{E}_{e}}$
3 ${{E}_{a}}={{E}_{e}}$
4 None of these
Explanation:
(b) We have ${{E}_{a}}=\frac{2kp}{{{r}^{3}}}$ and ${{E}_{e}}=\frac{kp}{{{r}^{3}}};\therefore {{E}_{a}}=2{{E}_{e}}$.
